GOAL PROGRAMMING AS A DECISION TOOL FOR NEW PRODUCTS PLANNING: A CASE EXAMPLE Ed Timmerman University of Tennessee at Martin Martin, Tennessee James A. Petty Abilene Christian University Abilene, Texas Applications of goal programming (GP) to marketing decision environments have been relatively rare, even though its composition makes GP eminently suitable for many marketing contexts. It appears that the technique could be particularly helpful in industries that specialize in advancing new technologies where marketing efforts are constantly undertaken in uncharted waters. The practical meaning of goal pro- gramming, for an industry dealing with new products designed for new markets and marketed in unfamiliar settings, is that this technique would aid in the generation of more rational product introduction decisions. The purpose of this article is to present and illustrate the use of goal programming as an aid to making common product introduction decisions, especially where techno- logically innovative products are concerned. First, is a description of the origin and primary elements of the linear goal programming, then a demonstration of how the tool can be applied to media choice and planning, and finally the procedure is utilized in a. promising industry (cellular communication) which is fraught with problems in- troduced by the accelerating advances in technology and ever shortening product life cycles. Background The concept of the profit maximizer, in classical economic theory, provides neither a sufficiently descriptive nor prescriptive model for the decision maker in a contempo- rary organizational setting. Since a broad range of goal categories may I'dCist, including economic, social, ethical, and political ones, as well as multiple elements within each category, it is hopeless to think of treating these in a linear fashion or to compare these at the same priority level. In this context, the decision maker is not trying to maximize, but to "satisfice." He is positioned as one attempting to attain a set of goals in an environment. The primary difficulty in decision analysis is the treatment of these multiple conflicting objectives. The task becomes one of value trades in the social structure of conflicting interests. Journal of Business Strategies, Volume 6, Number 1 (Spring 1989) 14 Spring 1989 Timmerman & Petty: Goal Programming 15 Goal programming, a modification and extension of linear programming, is a tech- nique for handling decision problems by means of a prioritized solution to a system of multiple conflicting objectives. The product of goal programming IS no substitute for a decision, but it does enable the one making the decisioo to be more systematic in attaining goals. Chames and Cooper [3], who were also pioneers in the application of tilled! pro- gramming (LP), originated the concept of goal programming. The conventional LP method utilized unidimensional objective functions (usually the maximizatIOn of prof- its or the minimization of costs) which proved excessively limiting where complex decision environments were the norm. The GP model they developed would handle multiple goals in multiple dimensions, therefore yielding a more leasible solution. Later Ijiri [7] contributed the notion of "preemptive priority factors" to allow treat- ment of multiple goals according to their importance, ..,signing weights to goals of the same priority level. His work refined the concept of goal programming and developed it as a distinct mathematical programming technique. Building upon this work, goal programming has found application in industrial and operations research settings, manpower and academic planning, management accounting, hospital admirnstration, and inventory control. Despite this foundation, applications of goal programming have been relatively scarce in the area of marketing. Exceptions to this occur in the areas of media plan- ning ([4], [5], [11]), sales effort allocation [16], and in retail store selection modeling [12]. The practical usc of the goal programming method has been considerably advanced by the work of three writers. Sang M. Lee's text of general applications for decision analysis [131 and a later management science text [14] have solidly installed the ap- proach as a standard decision tool. J. P. Ignizio's writings in the area of operations research ([8), [9], [10]) have also given the concept valuable exposure. And Marc J. Schniederjans book on linear goal programming [17J is a practical and helpful aid for the first time user. The software available with this text is especially useful. The Goal Programming Method The goal programming model consists of three basic components: a mathemati- cal expression of the weighted multiple goals to be achieved (objective function) the limitations or restrictions on achieving the desired goals (goal constramls), and the provision that negative solution values are not acceptable (non-negatiVIty require- ments). Using this approach, the algorithm seeks to minimize the deviations from each of a set of goals (objective criterion or function) subject to constraints imposed by the entire goal set (goal parameters or constraints imposed by limited resources, such as money, production capacity, time, etc., as restrictions on the ability to opti- mize the stated goals), rather than attempting to maximized or minimize an objective function directly. Additionally, there is an implicit requirement that all decision vari- ables take on non-negative values. This is appropriate for most marketing problems since they tend to deal with discrete variables. 16 Journal of Business Strategies Vol. 6, No.1 The most critical phase of the application of goal programming is the formulation of the model for the problem under consideration. In fact, considering the current availability of GP software, solution is not generally much of a difficulty once the model is constructed. Formulation of the model includes the following procedural elements: 1. Determine and specify whether the problem is one of maximization or minimiza- tion (as a rule, if the problem focuses on profit it is a maximization problem, or it on cost, it is a minimization problem). 2. Identify and define all factors relevant to the choice (decision variables) along with the amount each of these factors affect a decision (contribution coefficients). 3. State the goal (objective function) for the decision problem. 4. Identify and list the various constraints (also known as side constraints) working against the accomplishments of the goal. This usually shows up as limits on resource availability or resource usage. 5. Indicate that the resulting values of the decision cannot be negative by setting each of the decision variables equal to or greater than zero. The formulation for a media decision case will take the general form of a maxi- mization problem.! This goal mathematical programming procedure converges on an optimum solution within the constraints of the business environment. A critical difference in the GP approach and that of simple linear programming is that GP allows for a convex solution (i.e., one that expresses diminishing returns) which is much more realistic in most marketing contexts than a mere straight line solution. Complex problems are invariably multidimensional. IGoa] Programming Format for a Maximization Problem J Maximize: Z = 2:c) "') (objective function) j=l J subject to: 2: